To see the size of the log file, you can use FTP and go to the logs directory. All the logs will be there. My largest file is access_log, which I guess should usually be the largest file...
To set it to delete weekly, monthly, or never, go to your Plesk control panel, click on the domain (not for subdomains) you want to set, select Hosting, click Next, and choose your option under "Delete Apache Log Files".
As for what happen if you don't back it up, nothing would happen except you lose the information. It's just a log file, so your account won't go haywire or anything.
I seemed to have come across posts mentioning about Webalizer stats being started. Can't recall whether it is due to this deletion of logs, or log rotation (which I hardly know anything about). Didn't care much about it since I don't look at the Webalizer stats anyway.